Thoko's minibus timetable: latest safe bus and the term pass
Thoko lives in Ntaja and travels to school by minibus. She walks 20 minutes from home to the minibus stop. Minibuses to the school leave the stop at 06:00, 06:20, 06:40, 07:00 and 07:20, and the journey takes 35 minutes. From the place where the minibus drops her, Thoko walks 8 minutes to the school gate. The gate is closed and assembly begins at 07:30, and Thoko must be inside the gate before then. Thoko's mother buys her a term pass for MK 25 000, which covers every school day of the month. Without the pass, a single trip costs MK 700 and Thoko makes two trips a day, to school and home. The month has 20 school days. Thoko's friend says the pass is a waste of money 'because some days you are absent, and then you lose the money'.
1. Which is the latest minibus Thoko can take and still be inside the gate before 07:30? What time must she leave home, and how much spare time does she have?
Read the worked answer
Total time from leaving the stop to reaching the gate = 35 + 8 = 43 minutes. So the latest departure that still works must be no later than 07:30 − 43 min = 06:47.
Check from the timetable:
- 06:40: arrives 07:15 (06:40 + 35), at the gate 07:23 - 7 minutes early. ✔
- 07:00: arrives 07:35, at the gate 07:43 - 13 minutes late. ✘
Latest safe bus: 06:40.
She walks 20 minutes to the stop, so she must leave home by 06:40 − 20 min = 06:20. Leaving exactly at 06:20 leaves no spare time at the stop, so 06:15 is the sensible departure.
2. On rainy Wednesdays the minibuses run about 12 minutes late. How does that change Thoko's plan?
Read the worked answer
Apply the delay to the 06:40 bus: it leaves at 06:52, arrives at 07:27, and Thoko reaches the gate at 07:35 - 5 minutes late. Her 7-minute margin is smaller than the 12-minute delay, so the plan fails.
Next earlier bus, 06:20: delayed to 06:32, arrives 07:07, gate at 07:15 - 15 minutes early. ✔
So on Wednesdays she must catch the 06:20 bus and leave home by 06:20 − 20 min = 06:00.
Judgement: the 06:40 bus only works because of a 7-minute margin, which is thinner than the usual wet-season delay. The safe rule is to keep a margin bigger than the delay you expect (at least 12 minutes here), not to rely on the printed timetable. Working backwards from the deadline - 07:30 − 43 min − 12 min delay − 20 min walk - gives 06:15, and 06:00 adds a further 15 minutes of safety.
3. Was the MK 25 000 term pass worth buying? Support your answer with the break-even number of school days.
Read the worked answer
Daily fare = 2 × MK 700 = MK 1 400.
Over the 20 school days, fares without the pass = 20 × MK 1 400 = MK 28 000.
Saving from the pass = MK 28 000 − MK 25 000 = MK 3 000.
Break-even: MK 25 000 ÷ MK 1 400 = 17.86, so the pass is cheaper from 18 travel days upwards. Check: 18 days of fares = 18 × 1 400 = MK 25 200, just above the pass; 17 days = MK 23 800, just below it.
Judgement: yes, the pass is worth buying as long as Thoko travels at least 18 of the 20 days - she can miss up to 2 days and still gain. If she missed 3 days she would travel 17 days, pay MK 25 000 for the pass instead of MK 23 800 in fares, and lose MK 1 200. Her friend is only right if absences are frequent; occasional absence does not make the pass a waste.